Is there a way for attackers to win this? I've been playing single player easy and I always end up running out of time. Once I got a nuke in a crate which solved the 4 turrets but how do I defeat them without such luck?

Cooperation has gotten me (or rather, us) victory as attacker quite a few times on that map.

Can't speak for Single Player though, as I've only played it multiplayer.

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What I do (when there are no armours) is, I have 4-6 formations all lined up next to each other, and tell them all to attack at the same time - this means an attack from all accessible angles at once.

This usually won't get me the battle, but most of the time it gets me close enough to knock out a few turrets (or perhaps even gain control of one - which I then steer manually FOR GREAT JUSTICE).

A stream of unformationed Multiwinians can take out one or two turrets easy, so any left-over that didn't go in the first assault (I keep about 100-200 about two formationlengths behind) can come in and gain control of the now-knocked-out turrets.

You have to exploit the terrain. The more honest one would be hiding behind hills so that you're in range of the turrets but the turrets have no line of effect, getting you significantly closer to them, allowing a better shot at killing the MWs controlling them.
Throw in a distraction of visible MWs in the other direction for better results.
Getting some crates may help a lot.

At least, this is partly how I nearly lost.

At the the wall of turrets at the end, the other guy pretty much had to plant a flameturret behind the line of gunturrets and run straight at it from almost every angle. This burned everything.
I'm not sure what else would be effective here. Maybe a turret under manual control?

I find the best way to capture the wall of four turrets is to line a load of multiwinians up outside the laser fence while it is still up, then when it goes down there is no distance to cover, I've captured the four turrets within about 10 seconds of the wall going down this way

edit:: saying that, I still can't convincingly win the map against anything other than an easy CPU

GENERATION 22:The first time you see this, copy it into your sig on any forum and add 1 to the generation. Social experiment.

good tip on the ants and gernades behind force fields... however I still just don't have enough time to do it. Someone above posted that most posting on this board can complete this mission single player. I highly doubt it. I can do every level that Ive tried on easy and most on normal right now.

Well, I finally beat Third Kind as an attacker (single player). The trick was to use something from a crate on the green section that was guarded by gun turrets 2 deep (North West from where you start the game).

Begin the game as normal taking out the southern gun; and hope for an ant's nest or meteor shower from a crate while you're down there taking care of business. Green doesn't go back and try to replace the missing darwinians in that NW location. While your waiting for the right crate to do that, have all your troops waiting outside the shielded door to their base (North East where the UFO is). Then when the shields come down the overwhelming force of darwinians have either already taken out the guns behind the shields with gernades or quickly will after the shield comes down.

You really do have to rely on getting the right crate however. Otherwise, you just don't have enough time to get a decent group to go and take out the NW location and then finally the NE location. There's just not enough time.